I wish I spoke Russian, and I know this is difficult for you guys because to Russians and Czechs and Poles and Slovaks and Slovenians and anyone from around there it’s wholly senseless, but in English it’s vital and it will cost you marks in IELTS and there is no way round it.
‘I am Russian native speaker’ is and always will be wrong in English. It is not optional. You must include an article, in this case probably giving ‘I am a Russian native speaker…’; not impossibly 'I am the Russian native speaker…' Talking to hundreds of people from those nations above and more, my experience is that most find English articles not only a real challenge but fairly clearly, their greatest challenge. I completely sympathise; I wish it were not so but it is and any English proficiency exam will mark you down for messing up your articles.
What IELTS thinks about this next, I’ve no idea and ‘I am a Russian native speaker’ might be your worst choice. ‘I am a native Russian speaker’ is much better and ‘I am a native speaker of Russian’ might be best… depending on the context.
Strictly, that's why my sentence ‘might’ sound a bit weird would be at least twice as good if it used ‘may…’
‘… I wanted to reassure which one is exactly correct’ will never work. ‘Reassure’ can’t hover alone in space; it needs a person upon whom to act.
‘… I wanted to reassure myself which one… ’ could almost work but the statement would still need to match the tense of its own beginning.
‘… I wanted to reassure myself which one was exactly correct’ would almost work but ‘exactly’ isn’t helpful; it’s confusing.
‘… I wanted to reassure myself which one was correct’ works perfectly.
Going back to the OQ of ‘moved’ or ‘have moved’ both are acceptable in different contexts.
Broadly, ‘I moved’ describes something that I once did; ‘I have moved’ describes something that I have now finished doing.
Please look at http://www.verbix.com/webverbix/English/move.html